Summary In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.
Summary A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes.
In this research work, dynamic, mechanical, and thermophysical properties of untreated and 5, 7, and 10 wt % styrene treated tea dust (TD):polypropylene (PP) composites prepared by injection‐molding machine were elaborated. There were distinctive and significant improvement observed in mechanical properties (tensile strength, tensile modulus, and elongation at break), physical analysis (water swelling), dynamic mechanical properties (storage modulus, loss modulus, and tan δ), and thermal behavior and surface morphological properties of styrene treated TD:PP (40:60) composites as compared to that of untreated one. The tensile strength (from 7.00 to 9.95 MPa), tensile modulus (from 350 to 715 MPa), storage modulus (from 8500 to ∼10,500 MPa), and loss modulus (from ∼150 to ∼200 MPa) increased on 10 wt % styrene treatment of TD over the untreated TD:PP (40:60) composites. The styrene treated TD:PP (40:60) composites behaved as more elastic than their pure counterpart. Styrene treated TD:PP (40:60) composites were more thermally more stable (85 °C difference) as compared to virgin PP. Overall, this research also indicates the use of TD waste. An improvement in dispersion of styrene treated TD particles in PP was also observed in the preparation of the PP composites due to good compatibility of styrene with PP. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 44750.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.